The time for "strategic patience" with North Korea is over, US President Donald Trump warned Monday, after winning Japan's backing for his policy of considering all options to rein in the rogue state.

Trump described the North's nuclear programme as "a threat to the civilised world and international peace and stability" on the second day of an Asian tour dominated by the crisis.

The president has signalled in the past that Washington could look beyond a diplomatic solution to the North's nuclear weapons ambitions and consider military intervention.

"The era of strategic patience is over," he declared alongside his host, Japanese Prime MinisterShinzo Abe.

Washington in the past hoped that sanctions pressure and internal stresses in the isolated country would gradually bring about change. But critics said that policy gave Pyongyang room to push ahead with its nuclear ambitions.

Close ally Abe echoed Trump's remarks, voicing Japan's support for Washington's policy that "all options are on the table" to deal with the North Korean threat -- including military force.

Abe, whose country is under the path of North Korean missile launches, also announced Japanese sanctions on the assets of 35 North Korean groups and individuals.

The United Nations has adopted multiple rounds of sanctions against the reclusive North, the most recent in September following its sixth nuclear test and a flurry of missile launches.

Earlier, Trump had appeared to adopt a more conciliatory tone towards North Korea, saying he would not rule out talks with its bellicose young leader Kim Jong-Un.

"I would sit down with anybody," he said. "I don't think it's strength or weakness, I think sitting down with people is not a bad thing," he said in a television interview.

"So I would certainly be open to doing that but we'll see where it goes, I think we're far too early."

And the president again praised the "great people" of North Korea, adding "they are under a very repressive regime" and that he hoped it "works out for everyone".

But Pyongyang showed no sign of let-up in its attacks on Trump, with ruling party newspaper Rodong Sinmun calling him the "lunatic old man of the White House" and saying there was no telling when he would start a nuclear war.

'Golf diplomacy'

Abe and Trump's joint news conference capped two days of chummy behaviour in which the two golf fans have teed off for nine holes and enjoyed informal and relaxed dinners.

Abe said they had enjoyed each other's company so much over a dinner of scallops and steak on Sunday night that they lost track of time, while Trump said their relationship was "extraordinary".

At a state banquet Trump described the Japan leg of his marathon Asian tour as being like a "working vacation" and said he had enjoyed "every minute" of it.

"It's an honour. To have you as my good friend," said Trump.

The trip has also provided lighter moments, such as when Trump appeared to lose patience feeding koi carp at the Akasaka Palace and tipped his whole box into the pond, to the evident amusement of his secretary of state.

Aides had been concerned the unorthodox Trump would go off message or commit some gaffe in the famously rules-sensitive country.

But Trump sailed through a tricky protocol encounter with the emperor, greeting him with a slight nod and avoiding the criticism his predecessor Barack Obama got by bowing to the diminutive Japanese ruler.

Families of those abducted by North Korea clutched pictures of their loved ones

(POOL/AFP)

There were also moments of high emotion when Trump met the families of civilians abducted in the 1970s and 1980s, who were clutching pictures of their young family members.

A number of ordinary Japanese citizens were kidnapped by North Korean agents in order to train spies in Japanese language and culture.

Trump said he would do everything he could to secure their release and appeared to hold out the prospect of a deal with Kim.

"I think it would be a tremendous signal if Kim Jong-Un would send them back. If he would send them back, that would be the start of something very special," he said.

Despite the bonhomie, trade between the two nations remained a point of friction, with Trump earlier Monday blasting ties as "not fair and open" and saying that Tokyo had been "winning" for decades at the expense of the US.

"We seek equal and reliable access for American exports to Japan's market in order to eliminate our chronic trade imbalances and deficits with Japan," stressed Trump.

Trump can expect a more muted welcome from his next hosts in South Korea, where his relationship with President Moon Jae-In is cooler.

After that, he heads to Beijing for crunch talks with his Chinese counterpart Xi Jinping.

"I like him a lot. I call him a friend. He considers me a friend. With that being said, he represents China, I represent the United States," Trump said.